# Simple difference quotient question. Function -> simplify answer

1. Aug 28, 2012

### nukeman

Simple difference quotient question. Function --> simplify answer

1. The problem statement, all variables and given/known data

I just don't understand this question! Here, I will take a picture of it. Can someone please explain how I answer these? Or even show me a website that shows how to do these? Its not in my review book.

QUESTION is in ATTACHMENTS!

2. Relevant equations

3. The attempt at a solution

#### Attached Files:

• ###### photo (2).JPG
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2. Aug 28, 2012

### vela

Staff Emeritus
Re: Simple difference quotient question. Function --> simplify answer

It seems pretty straightforward what the question is asking. What specifically don't you understand?

3. Aug 28, 2012

### nukeman

Re: Simple difference quotient question. Function --> simplify answer

Can you tell me the first step? When you look at this, what is the first thing you see/do?

4. Aug 28, 2012

### vela

Staff Emeritus
Re: Simple difference quotient question. Function --> simplify answer

Exactly what the problem statement says: evaluate the difference quotient. If you don't understand what that means, try looking up "difference quotient" in your book.

5. Aug 28, 2012

### nukeman

Re: Simple difference quotient question. Function --> simplify answer

Must be missing something here.

I would plug in the f(x) values to the 2nd function, but there is no x's, just h ? How do I plug in values?

6. Aug 28, 2012

### Staff: Mentor

Re: Simple difference quotient question. Function --> simplify answer

The problem is asking you to evaluate the difference quotient to find f'(3).

7. Aug 28, 2012

### nukeman

Re: Simple difference quotient question. Function --> simplify answer

wow I'm lost. :(

8. Aug 28, 2012

### Macch

Re: Simple difference quotient question. Function --> simplify answer

Dude, f(x) = f(3+h) if x = 3+h

9. Aug 28, 2012

### Staff: Mentor

Re: Simple difference quotient question. Function --> simplify answer

The difference quotient to find the derivative of a function, f'(x), looks like this:

$$f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$$

The difference quotient to find the derivative of a function at a specific number a, f'(a), looks like this:

$$f'(a) = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}$$

10. Aug 28, 2012

### SammyS

Staff Emeritus
Re: Simple difference quotient question. Function --> simplify answer

Here's the image:

***************************

So, if $f(x)=4+3x-x^2\,,$ then what is $f(3+h)\ ?$

11. Aug 28, 2012

### nukeman

Re: Simple difference quotient question. Function --> simplify answer

SammyS, that is the one part I am having trouble fully understanding....

12. Aug 28, 2012

### vela

Staff Emeritus
Re: Simple difference quotient question. Function --> simplify answer

It would have helped if you could have said that right from the beginning.

In f(x)=4+3x-x2, the x is what's called a dummy variable. Anything you put in the lefthand side where the x is shows up wherever the x appears on the righthand side. For example, suppose you have g(x) = 2x+4. Then
\begin{align*}
g(y) = 2y+4 \\
g(h+3) = 2(h+3)+4 \\
g(4z) = 2(4z)+4 \\
g(weasel) = 2(weasel)+4 \\
g(3) = 2(3)+4 = 10
\end{align*}
Now tell us what you think f(3+h) is equal to in your problem.

13. Aug 28, 2012

### Staff: Mentor

Re: Simple difference quotient question. Function --> simplify answer

Apparently you don't understand how to evaluate a function's formula.

If g(t) = 3 - t2 (for example)
then g(1) = 3 - (1)2 = 3 - 1 = 2
and g(5) = 3 - (5)2 = 3 - 25 = -23
and g(a + 2) = 3 - (a + 2)2

So for your function, what is f(3 + h)?

14. Aug 28, 2012

### nukeman

Re: Simple difference quotient question. Function --> simplify answer

"So for your function, what is f(3 + h)?"

f(3+h) = 4 + 3(3+h) - (3+h)^2 ?

15. Aug 28, 2012

### Staff: Mentor

Re: Simple difference quotient question. Function --> simplify answer

Yes. You'll need to expand the right side and collect common terms.

16. Aug 28, 2012

### vela

Staff Emeritus
Re: Simple difference quotient question. Function --> simplify answer

Yup, that's it.